Importance of one-parameter hybrid exchange-correlation functionals in band gaps of transition metal and metalloid oxides

Importance of one-parameter hybrid exchange-correlation functionals in band gaps of transition...
Navarrete-López, Alejandra; Rivera-Almazo, Marcos; Garza, Jorge; Vargas, Rubicelia
2018-02-24 00:00:00
In this work, the effect of the exact exchange in hybrid functionals based on one parameter is explored over the electronic structure of
$$\hbox {Ti}_2\hbox {O}_3$$
Ti
2
O
3
,
$$\hbox {V}_2\hbox {O}_3$$
V
2
O
3
,
$$\hbox {Cr}_2\hbox {O}_3$$
Cr
2
O
3
,
$$\hbox {Fe}_2\hbox {O}_3$$
Fe
2
O
3
,
$$\hbox {MnO}, \hbox {SiO}_2$$
MnO
,
SiO
2
,
$$\hbox {GeO}_2$$
GeO
2
, and
$$\hbox {SnO}_2$$
SnO
2
, such that oxides with different nature are included in this data set. Structural parameters and magnetic states of these oxides are reproduced according to experimental information, which are discussed in the context of the exact exchange inclusion. Several exchange-correlation functionals are considered to reach this goal, two of them, HSE06 and B1WC, which were designed ad hoc to study metal oxides are contrasted with hybrid exchange-correlation functionals that contain a fraction (
$$\alpha $$
α
) of the exact exchange, like PBE0. Thus, in this work, hybrid functionals where
$$\alpha $$
α
is varied systematically provide a linear relationship between band gap and
$$\alpha $$
α
, which gives one way to match the theoretical band gap with experimental information. If this optimum
$$\alpha $$
α
is used to predict cell parameters or bulk modulus, then the corresponding results are close to experimental data. For the systems considered in this work, all-electron calculations were performed using a periodic ab initio code, which uses Gaussian localized basis set functions for the expansion of Bloch orbitals by linear combinations of atomic orbitals.
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Importance of one-parameter hybrid exchange-correlation functionals in band gaps of transition metal and metalloid oxides

Abstract

In this work, the effect of the exact exchange in hybrid functionals based on one parameter is explored over the electronic structure of
$$\hbox {Ti}_2\hbox {O}_3$$
Ti
2
O
3
,
$$\hbox {V}_2\hbox {O}_3$$
V
2
O
3
,
$$\hbox {Cr}_2\hbox {O}_3$$
Cr
2
O
3
,
$$\hbox {Fe}_2\hbox {O}_3$$
Fe
2
O
3
,
$$\hbox {MnO}, \hbox {SiO}_2$$
MnO
,
SiO
2
,
$$\hbox {GeO}_2$$
GeO
2
, and
$$\hbox {SnO}_2$$
SnO
2
, such that oxides with different nature are included in this data set. Structural parameters and magnetic states of these oxides are reproduced according to experimental information, which are discussed in the context of the exact exchange inclusion. Several exchange-correlation functionals are considered to reach this goal, two of them, HSE06 and B1WC, which were designed ad hoc to study metal oxides are contrasted with hybrid exchange-correlation functionals that contain a fraction (
$$\alpha $$
α
) of the exact exchange, like PBE0. Thus, in this work, hybrid functionals where
$$\alpha $$
α
is varied systematically provide a linear relationship between band gap and
$$\alpha $$
α
, which gives one way to match the theoretical band gap with experimental information. If this optimum
$$\alpha $$
α
is used to predict cell parameters or bulk modulus, then the corresponding results are close to experimental data. For the systems considered in this work, all-electron calculations were performed using a periodic ab initio code, which uses Gaussian localized basis set functions for the expansion of Bloch orbitals by linear combinations of atomic orbitals.